\section{Conclusion}
\label{sec:conclusion}

The initial choice of the approximated Hessian $B_{0}$ has a great influence on the convergence of the algorithm. We started with an identity matrix as approximation for the Hessian. Analysis of the eigenvalues of $B_k$ learned however that the eigenvalues of the true Hessian were distributed around $10^4$.  Multiplying the identity matrix by $10^4$ resulted in a much faster convergence.

The choice of the initial positions is also very important. If the problem is non-convex they will determine the outcome of the optimization routine. Also, the closer the initial positions $x_{0}$ are chosen to the final equilibrium position the fewer steps that are needed for the algorithm to converge. We are dealing with a physical problem for which we can intuitively estimate the minimum energy positions of the discrete points. Therefore it is advisable to choose the initial positions as the estimated positions. This will make the algorithm converge much faster.
Another option is to use the algorithm with few discrete points to compute a solution with low resolution. These points can then be interpolated and used as initial positions for a mesh with more discrete points. 
